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Essentially rigid floppy subgroups of the Baer-Specker group. (English) Zbl 0901.20043
The main result is that the countable direct product of the integers \(\mathbb{Z}^\omega\) contains a pure subgroup \(G\) with \(\text{End }G=\mathbb{Z}\oplus\text{Fin }G\), such that \(|\text{Hom }(G,\mathbb{Z})|=2^{\aleph_0}\) (here \(\text{Fin }G\) is the ideal of all endomorphisms of \(G\) of finite rank). This provides an answer to a question posed by Irwin, also previously solved by Blass and Göbel, under the assumption of the Continuum Hypothesis. The authors skilfully adapt already known results of others as well as of their own to prove the theorem.

20K25 Direct sums, direct products, etc. for abelian groups
20K30 Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups
03E50 Continuum hypothesis and Martin’s axiom
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